Prove that the value of 5cosa+3cos(a+π/3)+3 lies between -4 and 10

Hint:
!) use the formula of cos(A+B) = cosAcosB – sinAsinB for cos (a + pi/3)
2) then convert the given eq. in the form of mcosA + nsinA + c.
3) then its range will be in between: root(m²+ n² + c) to –root(m² + n² + c) .

Thanks, Vj